PC474 Optical Networks Laboratory

Power Measurements

Objectives

1. To review the measurement of power in optical systems.

Background

Power measurements are important in any situation involving data transmission.

Power is often expressed in decibels, where
P_dB = 10 log₁₀P

Logarithms make the units involved ambiguous, so in order to relate this to actual units, power can be expressed in dBm, where the power is measured in milliWatts. Thus
P_dBm = 10 log₁₀P(mW)

To convert back from dBm to mW, it should be obvious that
P_out (mW) = 10^P_dBm/10

Certain devices, such as amplifiers, can produce gain in a signal, meaning the output is greater than the input. In these cases, the gain is given by
A = P_out/P_in

It's often convenient to express gain in decibels, so
G_dB = 10 log₁₀(P_out/P_in)

In that case, to get the gain from the gain in decibels,
P_out/P_in = 10^P_dB/10
(Note that in this case P_out should be greater than P_in.)

Many things cause loss in a signal, and loss can be considered as negative gain, so
L_dB = - 10 log₁₀(P_out/P_in)

In that case, to get the loss from the loss in decibels,
P_out/P_in = 10^{- P_dB/10}
(Note that in this case P_out must be less than P_in.)

Attenuation loss is dependent on wavelength. For radio frequencies,
L_{attenuation-dB} = 10 log₁₀( (4 Π d)/λ²)
where d is the distance and λ is the wavelength.

Why use decibels?

At first glance, using decibels seems more complicated than using "normal" power units, such as Watts. However, when there are several elements in a system all producing gain or loss in a signal, it gets more complex. To get the final output of a system with several gains and losses, the original signal must be multiplied by the gain (or loss) of each element in the system. This can be tedious.
On the other hand, if you express everything in dB (or dBm), then gains and losses are represented by additions and subtractions.

Procedure

1. Fill in the missing quantities in the following table:

   Table 1: Power Measurements
   Power in (mW)	Power out (mW)	Gain (or loss) (dB)
   100	10
   15	0.2
   50		10
   	0.01	-30
   Related to those above
   10	100
   2	150
   0.01		30

   
   
   
2. In many situations, rather than having actual power measurements, it's easier to use percent (or fractional) changes in power. Fill in the missing quantities in the following table:

   Table 2: Power Measurements
   Percent change (%)	Fractional change	Gain (or loss) (dB)
   90	0.9
   10	0.1
   	2
   	0.01
   		5
   Related to those above
   	1/2
   	0.001

Before you leave the lab, have the lab instructor sign your lab notebook immediately after your last entry.